List questions from diophantine-equations

Published on 16 Apr 2026 - 4:56

104

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Condition for solution of Ramanujan–Nagell type equation

Published on 12 Apr 2026 - 15:28

43

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Solving Diophantine Equation $8^k={p+q}{p+q+4pq(p-q)}$

Published on 17 Apr 2026 - 10:34

657

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For which values of $a\in\mathbb{Q}$ does integer solutions to $x^2+x+1=a(y^2+1)$ exist?

Published on 17 Apr 2026 - 10:03

266

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maybe $(2^m-1)(3^n-1)$ can never be a perfect square?

Published on 16 Apr 2026 - 6:41

2.3k

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Quartic equation with integer solutions

Published on 27 Mar 2026 - 7:47

335

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Positive integers satisfying $a + b = c + d$ and $ab\vert cd$

Published on 16 Apr 2026 - 13:58

105

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Do the equations $X^4-2Y^4 = \pm Z^2$ have complete integer parameterizations?

Published on 16 Apr 2026 - 15:03

73

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Proof that $x^y=y^x$ is only true for the ordered pairs $(2,4)$ and $(4,2)$

Published on 16 Apr 2026 - 3:29

122

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Quadratic Diophantine Equation$(x^2+x)(y^2-1)=240$

Published on 16 Apr 2026 - 13:28

123

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$\{a+b|a,b\in\mathbb N^+\wedge ma^2+nb^2\in\mathbb P\}=\{k>1|\gcd(k,m+n)=1\}$

Published on 17 Apr 2026 - 4:14

94

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Solve $a\cdot 1111+b\cdot 111+c\cdot 11=9002$

Published on 17 Apr 2026 - 2:59

88

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To find all natural triples $(a, b, c)$ such that $2^c-1 \mid 2^a+2^b+1$

Published on 17 Apr 2026 - 9:10

1.6k

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Solve the equation $(2^m-1) = (2^n-1)k^2$

Published on 15 Apr 2026 - 8:26

255

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Solve in positive integers, $ x^6+x^3y^3-y^6+3xy(x^2-y^2)^2=1$

Published on 17 Apr 2026 - 8:20

List Question

When is $\sqrt[3]{a+\sqrt b}+\sqrt[3]{a-\sqrt b}$ an integer?

Condition for solution of Ramanujan–Nagell type equation

Solving Diophantine Equation $8^k={p+q}{p+q+4pq(p-q)}$

For which values of $a\in\mathbb{Q}$ does integer solutions to $x^2+x+1=a(y^2+1)$ exist?

maybe $(2^m-1)(3^n-1)$ can never be a perfect square?

Quartic equation with integer solutions

Positive integers satisfying $a + b = c + d$ and $ab\vert cd$

Do the equations $X^4-2Y^4 = \pm Z^2$ have complete integer parameterizations?

Proof that $x^y=y^x$ is only true for the ordered pairs $(2,4)$ and $(4,2)$

Quadratic Diophantine Equation$(x^2+x)(y^2-1)=240$

$\{a+b|a,b\in\mathbb N^+\wedge ma^2+nb^2\in\mathbb P\}=\{k>1|\gcd(k,m+n)=1\}$

Solve $a\cdot 1111+b\cdot 111+c\cdot 11=9002$

To find all natural triples $(a, b, c)$ such that $2^c-1 \mid 2^a+2^b+1$

Solve the equation $(2^m-1) = (2^n-1)k^2$

Solve in positive integers, $ x^6+x^3y^3-y^6+3xy(x^2-y^2)^2=1$

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